rheology and dna origami
TRANSCRIPT
DNA Origami and Rheology
Presented in fulfillment of requirements for graduation with Honors Undergraduate Research
Distinction in Chemical and Biomolecular Engineering at The Ohio State University
Submitted by: Patrick Kinnunen
Fall 2016
Faculty Advisor: Dr. Carlos Castro, Department of Mechanical and Aerospace Engineering
Graduate Advisor: Josh Johnson, Biophysics Graduate Program
Thesis Committee: Dr. Carlos Castro and Dr. Kurt Koelling, Department of Chemical and
Biomolecular Engineering
Abstract
The macro-scale behavior of engineering and biological materials is governed by the
composition of the constituent molecules. Therefore, understanding connections between behaviors at
different scales is of vital importance for understanding complex materials such as polymer solutions,
human tissue, or cellular cytoplasm. DNA origami, a technique which uses complementary base pairing
of deoxyribonucleic acid (DNA) molecules to build nanostructures with unprecedented spatial precision,
involves the combination of dozens of polymer molecules. In this work, the connection between DNA
origami, rheology, and material structure will be explored. Specifically, this thesis will work towards two
goals: Connecting the physical properties of DNA with the DNA origami folding process, and using a DNA
origami nanosensor to measure properties of the microenvironment. A two state DNA origami sensor,
called the Nanodyn, was designed which can change shape based on the presence of molecular
crowding agents in solution. The dynamics of the Nanodyn were measured in solutions with varying
weight percentages of polyethylene glycol (PEG) and it was shown that molecular crowding in solution
can be measured using a fluorescent assay. Full characterization of the Nanodyn will allow for the in situ
measurement of of biological materials. It also demonstrates the ability for DNA origami to study
rheological behavior. We also aimed to establish methods to study the viscoelastic properties of DNA
origami solutions. DNA origami structures are formed from hundreds of polymeric molecules, giving rise
to potentially complex rheological behaviors that could vary through the course of self-assembly. As a
foundation for studying complex DNA origami solutions, two techniques, bulk rheology and
microrheology, were applied to study simpler solutions containing DNA. Bulk rheology showed that DNA
has viscoelastic properties at concentrations relevant to DNA origami. However, the required sample
size makes it incompatible with current scales of DNA origami production. Microrheology allowed for
the measurement of solution viscosity and the microliter volume requirements make it highly amenable
for DNA origami, but methods need to be improved before they can be applied to quantitatively study
to DNA origami solution properties or self-assembly.
Acknowledgements
Firstly, I would like to thank Dr. Carlos Castro for his mentorship and encouragement over the
last two and a half years. From OhioMOD to the work presented here, His instruction and vision have
been imperative to my development as a scientist.
I would also like to thank Josh Johnson. He was crucial for the completion of this thesis, from
helping me with lab technique to the writing and editing of this document. More importantly, his
unending curiosity and dedication to discovery are a constant inspiration.
I would also like to acknowledge the contributions from the Koelling lab. Thanks to Dr. Koelling
for agreeing to serve on my thesis committee, and for allowing me to use the equipment in your lab. I
would also like to thank Varun Venoor for his instruction on the use of the rheometer.
None of this would have been possible without the whole lab – the atmosphere in NBL is
incredible. Specifically, I would like to thank Jenny Le for her help with my thesis proposal and thesis. Dr.
Mike Hudoba invented the Nanodyn, a major part of this work. Kelly Kolotka and Sarah Bushman helped
collect data for the Nanodyn chapter. Their diligence and hard work are appreciated, but not as much as
their company. Finally, Amjad Akif has been the source of many stimulating discussions, and I have tried
to approach research the same way he does since we started in OhioMOD together.
Lastly, I have to thank my family and friends. They kept me mostly sane for three years, to their
unending credit.
Contents Abstract ......................................................................................................................................................... 2
List of Tables and Figures .............................................................................................................................. 7
Chapter 1: Introduction – DNA and Viscoelasticity ...................................................................................... 9
Background ............................................................................................................................................... 9
DNA Origami ......................................................................................................................................... 9
Rheology ............................................................................................................................................. 16
Molecular Crowding: ........................................................................................................................... 22
Significance: ............................................................................................................................................ 24
Objective: ................................................................................................................................................ 25
Chapter 2: Molecular Crowding and DNA Origami ..................................................................................... 27
Introduction ............................................................................................................................................ 27
Background ............................................................................................................................................. 27
The Nanodyn: ...................................................................................................................................... 27
Förster Resonance Energy Transfer .................................................................................................... 29
Methods .................................................................................................................................................. 31
Structure Folding and Validation ........................................................................................................ 31
Fluorescence Measurements .............................................................................................................. 33
Results ..................................................................................................................................................... 34
Structure Folding ................................................................................................................................. 34
Fluorescence ....................................................................................................................................... 36
Discussion................................................................................................................................................ 39
Chapter 3: Bulk Viscoelasticity of DNA ....................................................................................................... 41
Introduction ............................................................................................................................................ 41
Background: ............................................................................................................................................ 41
Rheometers and Rheological Testing: ................................................................................................ 41
Viscoelasticity of DNA ......................................................................................................................... 44
Methods .................................................................................................................................................. 45
Rheological Measurements ................................................................................................................ 45
Results ..................................................................................................................................................... 46
Discussion................................................................................................................................................ 52
Chapter 4: Microrheology of DNA .............................................................................................................. 54
Background ............................................................................................................................................. 54
The Mathematics Behind Particle Diffusion ....................................................................................... 54
Particle Tracking .................................................................................................................................. 57
Methods .................................................................................................................................................. 58
Sample Preparation ............................................................................................................................ 58
Microscopy and Image Processing ...................................................................................................... 58
Results ..................................................................................................................................................... 59
Discussion................................................................................................................................................ 61
Conclusions and Future Work ..................................................................................................................... 63
Bibliography ................................................................................................................................................ 65
List of Tables and Figures Figure 1: The struture of double stranded DNA. Adapted from [1]. .......................................................... 10
Figure 2: A schematic of an immobilized Holliday junction, adopted from [4] . Half-arrows indicate the 5’
end of the DNA strand. ............................................................................................................................... 12
Figure 3: The design of a DNA origami plate. Top: The design of a single staple complementary to three
separate regions of the scaffold. Bottom: Scaffold routing, staple crossovers, and complementary staple
design. ......................................................................................................................................................... 13
Figure 4: Collage of DNA origami structures. (a): Patterns on a DNA lattice, (b): Protein binding on an
origami plate, (c): polymerization of DNA origami plates (d): Patterning of different macromolecules to
make an origami face. Modified from [9]. .................................................................................................. 14
Figure 5: Schematic of material properties in shear and tensile modes. Dotted line indicates original shape,
solid line indicates shape of material after deformation Δx and Δh due to force F applied over area A ... 17
Figure 6: Comparison of stress and strain rate in Newtonian and non-Newtonian fluids. Viscosity is the
ratio between stress and strain rate, the slope of the lines shown here. Newtonian fluids have a constant
viscosity, while shear-thinning fluids have a viscosity that declines as a power law. ................................ 18
Figure 7: Comparison of different theoretical materials when subject to oscillating strain. The stress in the
elastic material is perfectly in phase with the strain, while the viscous material is perfectly out of phase.
The viscoelastic material is somewhere in between (here the phase lag is π/3). ...................................... 20
Figure 8: Simplifying representation of a polymer of a series of beads and springs adapted from [20]. .. 21
Figure 9: Schematic of a polymer acting as an entropic spring. ΔS is the change in configuration entropy of
the polymer due to deformation or relaxation. ......................................................................................... 22
Figure 10: Large particles (Red) surrounded by solvent (grey). B: The excluded volume represents volume
inaccessible by solvent. Aggregation of large particles reduces exclusion volume. Modified from [22]. .. 23
Figure 10: Schematic of the Nanodyn. For clarity, only two of the six linkers are shown. Top left: Detail of
the fluorescent oligonucleotides used. Top right, bottom right: Demonstration of the ability to constrain
the Nanodyn. Bottom left: Cross section of the Nanodyn showing where the linker strands are. Modified
from [25]. .................................................................................................................................................... 28
Figure 11: The fluorescent spectra of Cy3 (left, donor) and Cy5 (right, acceptor), the FRET pair used in the
Nanodyn. The blue lines show the emission spectra of each molecule, while the red lines show the
emission spectra. The overlap (green) between the donor emission and the acceptor excitation spectra
allows FRET to occur. Typical FRET excitation (yellow) and detection (red) ranges are highlighted. Adapted
from [30]. .................................................................................................................................................... 30
Figure 12: Gel electrophoresis image showing successful folding of the Nanodyn. From left to right, the
lanes are: 10 kilobase DNA ladder, 8064 scaffold, Stock Nanodyn, Newly folded Nanodyn, 10 kilobase
ladder. Red box indicates similarity between new structures and previously validated structures. Excess
staples are seen near the bottom of the image. ........................................................................................ 34
Figure 13: TEM Image of several negatively stained Nanodyn structures in the open configuration. ...... 35
Figure 14: Bulk Fluorescence spectra for the donor and acceptor attached to the Nanodyn. The peak at
670 nm corresponds to the excitation of the donor. The red curve shows more acceptor excitation because
more of the Nanodyn are closed. ............................................................................................................... 36
Figure 16: Nanodyn FRET Efficiency as a function of PEG-8000 weight percent. ....................................... 37
Figure 17: Plot of FRET Efficiency vs Viscosity for the Nanodyn in varying PEG weight percentages. Viscosity
calculated from [33], [34]. .......................................................................................................................... 38
Figure 16: A representative schematic of a parallel plate rheometer. The oscillating motor typically
controls the bottom plate, while the top plate senses force. The sample (green) is held between the two
plates. Adapted from [42]. .......................................................................................................................... 42
Figure 17: Common rheometer geometries: parallel plates (A), cone and plate (B), couette (C). Adapted
from [43]. .................................................................................................................................................... 43
Figure 18: The results of changing DNA concentration on the stress-strain relationship of the solution.
Newtonian fluids have a constant linear stress-strain relationship. A decrease in slope is indicative of shear
thinning. Error bars represent one standard deviation based on three replicates. ................................... 47
Figure 19: Plot of G' and G'' of 13 kbp DNA strands measured in an oscillatory strain sweep on a shear
rheometer. Solid symbols are for G’, while open symbols are G’’. The oscillatory frequency was fixed at 1
rad/s. 1 dyne/cm2 is equivalent to 0.1 Pa*s. Modified from [44]............................................................... 48
Figure 20: Viscoelastic Moduli from strain sweep of -DNA at varying concentration. The data show a
decrease in the storage and loss moduli as concentration is decreased. Noise in the measurement
prevented data from lower concentrations being added. Error bars represent 1 standard deviation based
on 3 replicates. ............................................................................................................................................ 49
Figure 21: Average stress vs strain for triplicate strain sweeps of 3 mg/ml CT-DNA at 3 frequencies. Both
1 rad/sec and 10 rad/sec were very noisy, and no signal was detected at 100 rad/sec at low strain. ...... 51
Figure 22: Comparison of viscoelastic moduli in CT-DNA at varying concentrations. The data is very noisy,
and it appears as though the elastic and viscous moduli are constant over the range of strains studied
here. ............................................................................................................................................................ 52
Figure 23: Left: Representative frame of a microscopy video used for particle tracking. Right: Trajectories
aquired from MATLAB particle tracking script............................................................................................ 59
Figure 24: The trajectory of ten tracked beads is shown. In the picture above, the particle was tracked over
50 seconds. The displacement shown corresponds to a diffusivity of 2.28 µm2/sec. ................................ 60
Figure 25: The difference between accepted literature values and measured values for the viscosity of
water and 10% glycerol. .............................................................................................................................. 61
Chapter 1: Introduction – DNA and Viscoelasticity
Background
This thesis encompasses several aspects: polymer physics, DNA nanotechnology, rheology,
particle diffusion, and molecular crowding. Background information relating to all of these topics will be
introduced in the following section to give context for the thesis motivation. Each chapter will include
further background, which is relevant to the experimental details of the chapter.
DNA Origami
Deoxyribonucleic acid (DNA) molecules are biopolymers consisting of nucleotide monomers. The
nucleotides consist of three components: A phosphate group, a deoxygenated ribose sugar, and a
nitrogenous base. The first two are identical for any DNA nucleotide, but the nitrogenous base can be
any of four unique molecules: cytosine, guanine, adenine, or thymine. The nitrogenous base identifies
the nucleotide, and nucleotides are represented by the initial of their nucleobase: A for adenine, T for
thymine, G for guanine, and C for cytosine (Figure 1, right). Sequences of letters represent
polynucleotides with that sequence of bases. DNA strands have a directionality typically noted as 5’ to 3’
where the five prime (5’) end has a terminal phosphate, and the three prime (3’) end has a terminal
sugar.
Figure 1: The structure of double stranded DNA. Adapted from [1].
If two DNA molecules are complementary, they can form a double helix (Figure 1) [2].
Complementarity of DNA molecules is governed by their sequence of bases. Adenine and thymine are
complementary, as are cytosine and guanine. This complementarity is due primarily to two factors,
hydrogen bonding and molecular size. Adenine and Guanine are purines, larger molecules containing
two aromatic rings. Cytosine and thymine are pyrimidines, which are smaller and only have one
aromatic ring. Due to the size of the double helix, a purine can only be complementary with a
pyrimidine. Furthermore, A and T bind via two hydrogen bonds, while C and G bind via three. This
combination of size and energetic constraints enforces the complementarity of DNA base pairing (A-T, C-
G) [2]. DNA duplexes bind in an antiparallel configuration, with one strand running 5’ to 3’ and the other
strand running 3’ to 5’ (Fig. 1).
DNA double helix formation is a chemical reaction, with a corresponding change in free energy,
enthalpy, and entropy. There is a loss of entropy when two single-stranded DNA molecules combine,
which must be offset by binding interactions between the strands mediated in part by hydrogen
bonding between bases. They are also stabilized by base stacking – the interaction of pi orbital electrons
in successive bases [3]. The double helix constrains the geometry of the DNA, enabling base stacking
interactions. Repulsion between the negatively charged phosphate backbones of DNA duplexes also
creates an energetic cost for the formation of a DNA duplex. Thus, DNA duplexes must form in solution
with positive ions, which screen the repulsions the negative phosphate group and stabilizes the double
helix. This is particularly important for DNA assemblies like DNA origami where many helices are being
packed tightly together. For DNA strands to self-assemble, the favorable energetic interactions from
forming a DNA duplex must off-set the unfavorable loss of entropy and electrostatics. Since the effect of
entropy is temperature-dependent, DNA duplexes will melt at a high enough temperature. The melting
temperature occurs at the point where entropic effects overcome the stabilizing interactions of the
duplex, causing it to fall apart. It is also worth noting that DNA duplexes do not require perfect
complementarity between strands to form. As long as the stabilizing interactions between strands are
greater than the loss of entropy at a given temperature, the duplex can form. It is also possible for a
DNA strand to bind to itself, forming a hairpin loop, if two portions of the same single-stranded DNA are
complementary. These variations on DNA secondary structures become important considerations in the
design of DNA nanostructures, and in some cases they can be exploited to enhance the function of DNA
nanodevices.
The first use of DNA as a nanoscale structural material was published by Nadrian Seeman in
1982 [4]. He used immobilized Holliday junctions to create repeating lattices of DNA. A Holliday junction
is a naturally occurring DNA structure which integrates four single-stranded DNA molecules (Figure 2).
Figure 2: A schematic of an immobilized Holliday junction, adopted from [4] . Half-arrows indicate the 5’ end of the DNA strand.
As shown in Figure 2, each DNA strand forms a double helix with two of the other strands. DNA
molecules can be designed to create 2-D and 3-D DNA structures incorporating repeating Holliday
junction motifs.
DNA origami nanostructures usually consist of several helices created by the base pairing of
complementary DNA to form a series of stacked Holliday junctions. The technique was first introduced
by Paul Rothemund in 2006 [5]. One loop of DNA, the scaffold, runs continuously through the whole
structure. The scaffold, typically derived from the M13mp18 bacteriophage genome, has a length of
7000-8000 bases [6]. The wild type genome is 7249 bases with a fully known sequence. The length of
the scaffold can be modified with specific DNA inserts which also have a known sequence. Based on the
desired shape and the sequence of the scaffold, individual oligonucleotides known as staples can be
synthesized which are complementary to specific parts of the scaffold. The staples bind to the scaffold in
a piecewise complementary manner, pulling it into the desired shape (Figure 3, a DNA origami plate).
Figure 3: The design of a DNA origami plate. Top: The design of a single staple complementary to three separate regions of the scaffold. Bottom: Scaffold routing, staple crossovers, and complementary staple design.
The staples are designed such that they will cross over between adjacent double helices, stabilizing the
structure. The placement and number of these cross overs is one contributor of structure viability – if
there are not enough, the adjacent double helices will not be held together and the structure will not
form.
To make DNA nanostructures, the scaffold and staples are first combined in a buffered salt
solution [7]. The salt, typically MgCl2, contributes cations to solution, which are necessary to stabilize the
formation of double helices. DNA origami is folded in a thermal ramp, where it is typically heated to
65°C and cooled over a time period that can vary from hours to a few days. Initially, the high
temperature of the thermal ramp melts DNA binding interactions including secondary structure of the
scaffold or staples. Secondary structure refers to instances in the scaffold or staples where there is self-
complementarity and the DNA forms loops. Secondary structure in the scaffold or staples make it very
unlikely that scaffold-staple binding will occur, and hence inhibits the formation of the desired
nanostructure. The cooling step allows the staples to anneal to the desired region of the scaffold. The
annealing of different staples takes place at different temperatures, partially governed by the base
sequence of the double helix. Staple annealing is also cooperative; as staples bind with the scaffold, they
constrain the scaffold loop and making it easier for other staples to bind [8].
DNA origami has developed substantially since it was first introduced in 2006. Rothemund
initially demonstrated the flexibility of DNA origami by designing and synthesizing a number of two
dimensional DNA origami structures including a rectangles, smiley faces, and triangles composed of
adjacent DNA helices [5]. Further developments led to greater control over static DNA shapes, and the
synthesis of three-dimensional shapes [6].
Figure 4: Collage of DNA origami structures. (a): Patterns on a DNA lattice, (b): Protein binding on an origami plate, (c): polymerization of DNA origami plates (d): Patterning of different macromolecules to make an origami face. Modified from [9].
In ten years, the scope of DNA origami has expanded dramatically (figure 4). DNA robots have been
developed, which can undergo actuated conformational changes or walk along a pathway [10], [11].
DNA origami structures have been built which incorporate fluorophores or nanoparticles which can
serve as sensors [12]. Several promising drug delivery devices have been produced which incorporate
targeting and controlled release [13], [14]. These devices have shown great promise in in vivo mouse
trials.
The simplicity of the DNA origami folding process belies the complexity of the reactions
occurring to create the nanostructures. For every binding interaction between a portion of the scaffold
and a portion of a staple, there is a thermodynamic equilibrium between bound and unbound DNA
governed by the DNA base sequence. The temperature at which binding will occur is determined by the
base sequence in addition to other factors such as scaffold looping entropy and cooperative binding
effects. In addition to thermodynamic considerations, so called “Kinetic traps” can arise trapping the
DNA origami structure in misfolded states that are local energy minima [7]. Kinetic traps were relatively
easy to avoid for early 2D DNA origami structures, because the scaffold generally adopts a simple
topology in the final structure. However, more complex shapes require more complex scaffold
topologies giving rise to more complicated folding pathways and a higher probability of kinetic traps.
Theoretical frameworks to understand DNA origami self-assembly and structure properties have
necessarily advanced. The effect of staple arrangements on structure folding and cooperativity was
explored by Wei et. al. and it was shown that energetically identical staples with different crossover
locations change the overall thermodynamics of an origami structure [8]. Song et. al. demonstrated
isothermal origami assembly at viable yield by changing the chemical composition of the solution [15].
Finally, Marras et al. showed that deliberate manipulation of the folding pathway of an origami structure
can enable the creation of complex structures that are otherwise energetically unfavorable [16].
However, no one has studied the bulk physical properties of solutions containing DNA origami staples,
scaffold, or folded structures. DNA origami nanostructures are essentially rigid, while DNA molecules act
as flexible chains in solution [17], [18]. The transition is gradual – different double-helical domains form
as individual staples bind, gradually constraining the scaffold until it forms a well-folded, rigid structure.
Studying this transition may provide new insights into how DNA origami structures form.
Rheology
Rheology is the study of the flow of matter. This can mean anything from the high temperature
material creep of steel beams to the flow of water, but rheological measurements are most often used
to study complex materials like colloid suspensions, solid and liquid polymers, and biological materials. A
macro scale deformation of a material is generally a result of changes in the underlying structure down
to the molecular scale, meaning that rheological measurements are fundamentally linked to the
molecular character of the material. For polymers in solution, imposing a force on the bulk solution
causes individual polymers to deform and changes in intermolecular interactions mediated by
entanglements, cross-links or hydrodynamics. As a polymer, DNA can undergo similar deformation or
interactions with the environment, and hence can be characterized by rheology.
Rheological measurements typically involve the application of a force and the measurement of
the resulting deformation, or the measurement of a force required to achieve a specific deformation.
For instance, a rubber sample will be stretched to double its length, and the required force will be
measured. A critical feature of rheological measurements is the time scale and directionality of the
imposed force or deformation and corresponding material response. As an example, stretching a sample
of silly putty or bread dough by some amount over the time scale of a day might require less force than
stretching that sample the same amount over the timescale of a second. This is an example of a
viscoelastic material. In some cases, the direction of the test is also important. For example,
deformation under an applied tension may be governed by a different material property than twisting
under a shear force or contraction under compressive force. This is an example of an anisotropic
material.
Applied forces are typically expressed as stress, the force per unit area, and deformation is
typically expressed as dimensionless strain. Rheological measurements typically quantify a relation
between force and deformation, often characterized as a modulus – the ratio of stress to strain.
Figure 5: Schematic of material properties in shear and tensile modes. Dotted line indicates original shape, solid line indicates shape of material after deformation Δx and Δh due to force F applied over area A
A familiar example of a modulus is the elastic spring constant, where the modulus is the ratio of force to
spring deformation. A stiff spring has a higher modulus. A schematic showing stress and strain in tensile
and shear modes is given in figure 5. Based on figure 5, the equations relating stress (equation 1), strain
(equation 2), and modulus (equation 3) in shear and tensile tests are:
Shear Tensile
Stress: 𝜏 =𝐹
𝐴 𝜎 =
𝐹
𝐴
(1)
Strain: 𝛾 =∆𝑥
ℎ 𝜖 =
∆ℎ
ℎ
(2)
Modulus: 𝐺 =𝜏
𝛾 𝐸 =
𝜎
𝜖 (3)
Strain, being a ratio of displacements, is dimensionless. Stress and modulus both have units of pressure.
Characterization of stress versus strain relations are some of the most fundamental rheological
measurements, but they are not sufficient for the study of polymer solutions. Another important
measurement is viscosity, the resistance of a fluid to flow. Whereas the modulus of a material is the
ratio of stress to strain, viscosity is the ratio of shear stress to shear strain rate (Equation 4).
𝜂 =𝜏
�̇� (4)
In a highly viscous fluid, more stress will be required to cause the fluid to flow at a given rate than in a
low viscosity fluid. Viscosity can also be a function of shear rate, as is demonstrated in figure 6, below.
Figure 6: Comparison of stress and strain rate in Newtonian and non-Newtonian fluids. Viscosity is the ratio between stress and strain rate, the slope of the lines shown here. Newtonian fluids have a constant viscosity, while shear-thinning fluids have a
viscosity that declines as a power law.
The viscosity of Newtonian fluids is independent of strain rate – twice as much shear stress will double
the shear strain rate. However, this relationship does not hold for a shear thinning fluid, which is typical
of a high concentration polymer solution. At low shear rates, the viscosity of a concentrated polymer
solution is relatively high. This is due to the entanglement of polymer molecules and the greater degree
of interaction between polymers in an equilibrium configuration. However, as shear is continuously
applied, the entanglements of molecules are broken and the individual molecules are deformed into a
straighter configuration, where polymer molecules can slide past each other relatively easily. This leads
to a decrease in viscosity. Similar molecular deformations can lead to strain hardening in polymeric
solids since polymers become harder to stretch once they are closed to their extended configuration or
can undergo strain induced crystallization once molecules are aligned under deformation.
Some materials can be described by adequately by either their modulus – as in a steel beam, or
their viscosity – as with a Newtonian fluid like water. However, most materials have viscous and elastic
qualities. They are viscoelastic. Rheology is primarily concerned with the measure of viscoelasticity in
solid and liquid samples. Viscoelasticity is typically measured using oscillatory stress or strain. In an
oscillatory strain test, the applied shear strain (equation 5) and shear strain rate (equation 6) are
described by the following equations:
𝛾 = 𝛾0sin(𝜔𝑡) (5)
�̇� = 𝛾0ωcos(𝜔𝑡) (6)
where ω is the frequency of oscillation and γ0 is the maximum strain magnitude. The resulting stress in a
viscoelastic material is then given by:
𝜏 = 𝜏0sin(𝜔𝑡 + 𝛿) (7)
where δ is the phase lag. For a perfectly elastic material, the phase lag will be zero – the stress will be
exactly in phase with the applied strain. For an entirely viscous material, stress is related to the
derivative of the strain, so the phase lag will be 90°. A viscoelastic material will have a phase lag
between 0° and 90°, corresponding to the relative energy dissipation and storage. Each of these
behaviors is shown in Figure 7.
Figure 7: Comparison of different theoretical materials when subject to oscillating strain. The stress in the elastic material is perfectly in phase with the strain, while the viscous material is perfectly out of phase. The viscoelastic material is somewhere in
between (here the phase lag is π/3).
From the phase lag, storage modulus G’ and loss modulus G’’ are defined in equations 8 and 9, below.
The storage modulus is the component of the modulus which is in phase with the strain, while the loss
modulus is the component that is 90° out of phase with the strain.
𝐺′ =𝜏0𝛾0cos(𝛿) (8)
𝐺′′ =𝜏0𝛾0sin(𝛿) (9)
The same conventions for shear and tensile modes hold; when referring to moduli, G denotes shear
while E denotes tensile modulus.
There are several models that account for the viscoelasticity of polymer solutions. One of the
simplest, the rouse model, treats polymers as a series of beads and springs (figure 8) [19]. The springs
model the polymer elasticity, while the beads experience viscous hydrodynamic drag.
Figure 8: Simplifying representation of a polymer of a series of beads and springs adapted from [20].
For the Rouse model the polymer chain is broken down into segments where each segment behaves as
an elastic spring. The rouse model is only applicable when the length of the chain is much greater than
the length of each subunit. The beads capture the energy is dissipated from the hydrodynamic drag the
chain experiences as it moves through the solution, while the springs capture the energy stored via the
entropic elasticity of the polymer. The rouse model can be used to understand how a macromolecule
behaves in a solution subject to flow. The beads are subject to hydrodynamic drag forces, causing the
molecule to align with the flow and stretching the springs connecting the beads. The stretched springs
store energy. When flow stops, the stretched springs relax, causing the beads to move. The beads once
again experience drag forces, dissipating some of the energy stored.
In solution, polymer molecules have an equilibrium distribution of conformations. The most
likely conformation at equilibrium represents the minimum free energy for the chain, which is a function
of the configurational entropy of the chain, interactions between the polymer and the solvent, and any
potential inter- or intra-molecular interactions. Ignoring intra- or inter-molecular interactions, when the
polymer is deformed, the configurational entropy is decreased.
Figure 9: Schematic of a polymer acting as an entropic spring. ΔS is the change in configuration entropy of the polymer due to deformation or relaxation.
Therefore, increasing entropy acts as a restoring force for the molecule. This process is shown for an
individual macromolecule in figure 9.
The Rouse model was conceived to describe the behavior of dilute polymers in solution. In this
case, dilute has a very specific meaning: separate polymer chains do not interact. Significant interactions
between polymers lead to longer timescale behaviors that the Rouse model cannot account for. The
overlap concentration, c*, which is the concentration where polymer molecules start to overlap can be
approximated by the formula:
𝑐∗ =
𝜌𝑁
𝑅𝑔3
(10)
where ρ is the mass density of the chain, N is the number of monomer units in the chain, and Rg is the
radius of gyration for the molecule [21]. The radius of gyration is a measure of the average distance
from the polymer center of mass to a monomer unit.
Molecular Crowding:
The presence of macromolecules in solution can cause polymers to store or dissipate energy
differently, affecting their rheology. However, macromolecules in solution are also responsible for
another effect: molecular crowding. Molecular crowding leads to depletion forces that tend to be
compressive forces on a molecule or structure. Depletion forces arise in solutions of macromolecular
solutes surrounded by relatively smaller molecules that are on the same size scale (Figure 10). These
molecules are typically represented as hard spheres with dimensions given by the interaction distance of
the molecule.
Figure 10: Large particles (Red) surrounded by solvent (grey). B: The excluded volume represents volume inaccessible by solvent. Aggregation of large particles reduces exclusion volume. Modified from [22].
Depletion forces are typically understood as totally entropic. As shown in figure 10, there is
some excluded volume surrounding each macromolecule, and at the border of the box. The excluded
volume is space that is inaccessible to crowding molecules due to their size. The maximum entropy of
the full system is related to the volume accessible by the crowding molecules. Minimizing the excluded
volume leads to higher entropy of the crowding molecules. The excluded volume in the system is a
function of the size of the crowding molecule and the size of the macromolecule. Assuming neither
changes size, the excluded volume due to an individual macromolecule cannot be changed. However,
when macromolecules aggregate their excluded volume overlaps (Figure 10), decreasing the total
excluded volume in the system. Reducing the excluded volume also reduces the entropy, giving rise to a
depletion forces pushing the macromolecules together that is a function of the crowding molecule
concentration.
Cells are full of macromolecules of different compositions, so it is unsurprising that depletion
forces are significant in many cellular functions. It has been shown that molecular crowding forces are
comparable to the forces involved in many cellular activities. For instance, the formation of higher order
structures in proteins and DNA, and it has been shown that molecular crowding increases the rate of
refolding of various enzymes [22]. Crowding molecules increase the melting temperature of DNA
duplexes and affect organization of DNA at the chromatin level [23]. There are several other examples of
molecular crowding contributing to biochemical phenomena in literature.
Significance:
DNA origami clearly has potential to address many critical challenges in medicine and
nanoscience, including drug delivery, diagnosis, and molecular detection. More visionary applications of
DNA origami include information storage and computing. A better understanding of the self-assembly
process to maximize yield, efficiency, repeatability, and scalability is essential for DNA origami to leave
the lab and fulfill its industrial and clinical potential.
DNA origami folding is complex. Dozens of polymer molecules bind non-covalently. The
configuration of the polymers must change to accommodate these new bonds. Due to the energy
involved in staple binding and the topology of the molecules, subtle changes in staple arrangement can
yield very different results. The analysis of DNA binding is further complicated by the chemical nature of
the bonds formed. Double helices are stabilized by hydrogen bonding between adjacent bases, and all of
the hydrogen bonds are essentially identical. Given the similarity of bonds formed, typical spectroscopic
methods are useless for differentiating between them. By conjugating a fluorophore to a specific staple,
the binding of that staple can be studied, but this approach does not scale well given that more than one
hundred staples are involved with origami folding. The chemical binding of two different staples is
almost identical, but their effect on the scaffold can be very different. One staple might pull three
separate regions of the scaffold together in space, while another one might bind to one continuous
region of the scaffold, having very little effect on the scaffold shape. Therefore, exploring the physical
effect of staple binding may provide new insight into understanding and optimizing DNA origami folding.
Molecular crowding and rheology are intimately connected. The hierarchal folding of proteins
bears some resemblance to the cooperative folding of DNA origami. Therefore, determining if crowding
could be used to influence origami folding could improve the yield of origami folding or allow for the
formation of new structures. For instance, the binding of DNA origami staples is concentration
dependent, and putting more of a particular staple in solution will increase the rate at which that
particular staple binds. However, staples may also act as crowding agents, and crowding may affect the
conformation of the scaffold, inhibiting folding. Improving the understanding of DNA viscoelasticity and
its relationship with molecular crowding could also be beneficial for enhancing DNA origami production.
Furthermore, because folded DNA origami structures are affected by molecular crowding it
should be possible to study the effects of molecular crowding, and consequently rheology, using DNA
origami nanostructures. DNA origami is inherently biocompatible and other applications of DNA origami
have demonstrated that it is stable in cell cytosol for hours [24]. DNA origami could be used to measure
the effects of molecular crowding and rheology in cells, which would provide valuable new
understanding related to how cellular viscoelasticity affects cellular processes.
Objective:
This thesis will work towards connecting rheology and molecular crowding with DNA origami.
The long-term goal of this work is to test how the rheology of a DNA origami solution changes as it forms
compact nanostructures from disparate strands of DNA. I hypothesize that, as the scaffold and staple
molecules become more constrained, their behavior will change. Specifically, the conformations of the
DNA stands in solution is changing, which should affect their interactions both with the solvent and
other molecules, and the number of bulk staples in solution decreases, likely leading to less energy
dissipation.
Along with studying the evolution of rheological properties during folding, the effect of physical
interactions with surrounding solvent on folded DNA origami nanostructures was studied. A two state
(open/closed) nanostructure called the Nanodyn had been developed previously [25]. It has been
demonstrated that the Nanodyn conformation is sensitive to changes in viscosity. The sensor shows
potential for studying viscoelasticity and molecular crowding, but it needs to be fully characterized.
Therefore, the variation in sensor output was measured over a range of viscosities. Viscosity was
controlled by changing the amount of polyethylene glycol in solution. This work will contribute to the
use of the sensor for measuring the viscoelastic properties of collagen matrices. Collagen is a structural
protein which is common in the extracellular matrix. It has been shown that reorganization of collagen
and stiffening of tissue is a characteristic of tumors, but it is difficult to measure that stiffening locally
[26]. Measuring the behavior of the Nanodyn implanted in collagen may improve our understanding of
the role of tissue stiffening in cancer.
Chapter 2: Molecular Crowding and DNA Origami
Introduction
Dynamic DNA origami devices typically have a distribution of configurations defined by the
energy landscape of the structure [27]. Given the comparable size of DNA origami and biomolecules, it is
likely that the conformation DNA origami could be affected by molecular crowding. Therefore, the use
of DNA origami for studying molecular crowding was explored.
Background
The design and functionality of the DNA origami device will be detailed in the following section,
and background will be given for the analysis methods used for the device.
The Nanodyn:
The NanoDyn, a DNA origami device developed at Ohio State by Dr. Michael Hudoba, was used
to test the hypothesis that DNA origami nanostructures are affected by molecular crowding [25]. The
NanoDyn is a two state (open/closed) nanostructure that incorporates fluorescent molecules to indicate
the state of the device. Each barrel of the Nanodyn has a 24 helix bundle cross-section, and the barrels
are approximately 50 nm long (Figure 11). The barrels are connected by six scaffold loops arranged
radially around the barrels. Each scaffold loop is relatively unconstrained, allowing the barrel to switch
between the open state, where the barrels are far apart, and the closed state, where they are close
together.
The addition of constraining staples can specifically modify the dynamics of the device. Typically,
staples are added that are complementary to the scaffold loop, turning into two dsDNA duplex sections
connected end-to-end but separated by a few ssDNA bases to facilitate flexible motion between the two
barrel components. Alternatively, constraining staples can be added to pull individual scaffold loop
together, forcing the device to close and biasing the conformation of the device overwhelmingly
towards the closed state. Further details relating to the Nanodyn can be found in reference [25].
Figure 11: Schematic of the Nanodyn. For clarity, only two of the six linkers are shown. Top left: Detail of the fluorescent oligonucleotides used. Top right, bottom right: Demonstration of the ability to constrain the Nanodyn. Bottom left: Cross section
of the Nanodyn showing where the linker strands are. Modified from [25].
The loops can also be constrained using fluctuating staples – these staples are designed to bind with a
high affinity to one portion of the scaffold loop, while binding transiently with another portion (figure
11, top left). The fluctuating linkers impart dynamic opening and closing behavior where the dwell times
in the closed state can easily be tuned by the strength of the transient binding interaction. For example,
a fluctuating linker binding between eight nucleotides will close for a very short time that might not
even be detectible with typical measurement methods. Alternatively considering many Nanodyn devices
at a single point in time, only a very small fraction would be closed. In contrast, a longer connection of
twelve bases would lead to longer dwell times in the closed state, or close a much larger portion of the
population at a single point in time. We assume the opening/closing is an ergodic process such that the
behavior of a single device over long times can recapitulate similar behavior compared to considering
many devices at a single point in time. In addition, up to five scaffold loops can be constrained
individually (Fig. 11, bottom right), giving precise control over the dynamics of the device.
Förster Resonance Energy Transfer
By conjugating the fluctuating linker staples with fluorescent molecules, the dynamics of the
device can be studied using fluorescence-based techniques. Two fluorescent molecules can interact
when they are very close (<10 nm), in a phenomena known as Förster resonance energy transfer (FRET)
[28], [29]. The interaction is a strong function of distance, meaning that FRET can be used to detect
changes in distance at the nanoscale.
FRET is the non-radiative transfer of energy between two fluorescent molecules, a donor and an
acceptor. Any fluorescent molecule has a characteristic absorption and emission spectra, which
describes the range of wavelengths of light that can excite it and the range of wavelengths it will emit
light at. FRET is a function of spectral overlap between the donor emission spectrum and acceptor
excitation spectrum. The fluorescence spectra of Cy3 and Cy5 is shown in the following figure (Figure
12).
Figure 12: The fluorescent spectra of Cy3 (left, donor) and Cy5 (right, acceptor), the FRET pair used in the Nanodyn. The blue lines show the emission spectra of each molecule, while the red lines show the emission spectra. The overlap (green) between
the donor emission and the acceptor excitation spectra allows FRET to occur. Typical FRET excitation (yellow) and detection (red) ranges are highlighted. Adapted from [30].
Due to the large spectral overlap between Cy3 and Cy5, they are commonly used as a FRET pair and
were incorporated into the Nanodyn. FRET is typically expressed as a normalized efficiency representing
the amount of energy transferred from the donor to the acceptor normalized by the total intensity
emitted by the combination of donor and acceptor.
FRET interactions are mediated by several factors other than spectral overlap, with distance
being the most significant. The FRET efficiency for a single FRET pair is given the following formula:
𝐸𝐹𝑅𝐸𝑇 =
𝑅06
𝑅06 + 𝑟6
(11)
Where r is the distance between the fluorophores and R0 is a dye specific constant related to the
quantum yield of the donor dye, the orientation of the molecules, and the degree of overlap of the
spectra of the dyes. The sensitivity of FRET to distance is caused by the dependency on distance to the
sixth power, causing FRET efficiency to drop to approximately zero very quickly as the donor and
acceptor separate.
Binding of the fluctuating linker will force the Nanodyn into its closed conformation, and
dissociation of the fluctuating linker allows the structure is open. The displacements between the open
and closed state are on the scale of ~10 nm, making FRET an appropriate readout. In the Nanodyn, the
fluctuating staple is conjugated with one fluorophore, while the other fluorophore is conjugated with a
staple that binds permanently with the scaffold loop (Figure 11). Therefore FRET efficiency will be
directly correlated to the proportion of Nanodyn structures in the closed conformation. The fluorescent
functionality of the Nanodyn is beneficial for several reasons. The conformation of the device can be
observed and measured using other methods such as transmission electron microscopy (TEM), but
those methods are typically incompatible with biological samples. Fluorescence is commonly used in
biological assays, meaning the Nanodyn could be easily integrated into many biological systems.
Methods
There were several requirements for testing the hypothesis that the Nanodyn is sensitive to
molecular crowding. Viable structures needed to be folded, purified, and validated. The solution
viscosity needed to be controlled in a way that was compatible with DNA origami. Finally, the
fluorescent output of the structures needed to be measured.
Structure Folding and Validation
The Nanodyn is designed to be folded with an 8,064 base long scaffold, and the oligonucleotides used to
fold the structure were designed previously. Several aspects of the Nanodyn folding process have also
been optimized previously [25]. Based on this previous work, the Nanodyn was folded at 18 mM MgCl2
concentration. A 65 hour thermal ramp from 65°C to 4°C was used to fold the structure. The structure
was folded at 20 nM scaffold concentration with 10x excess staples in folding buffer (5 mM TRIS, 1 mM
EDTA, 18 mM MgCl2, 5 mM NaCl) according to a standard procedure found in literature [7].
After structures were folded, they needed to be validated. Agarose gel electrophoresis is a
method that applies a charge across a gel containing DNA samples. The negative charge of DNA causes it
to migrate towards a positive electrode, while the size of the DNA changes the rate of migration. DNA
origami structures are much more compact than the scaffold, so structures typically migrate more
quickly than the scaffold but can vary depending on the specific geometry of the origami structure. The
gels used to validate DNA origami were 2% agarose, made with .5X Tris-Borate-EDTA buffer and 11 mM
MgCl2. The gel was run at 70 volts until the scaffold and staples had sufficient time to separate.
Structure validation was further accomplished using transmission electron microscopy (TEM) [7].
For imaging DNA origami, the structures are deposited on a copper mesh grid, and 2% uranyl formate is
subsequently added to produce a negative stain. The heavy uranium nuclei deflect the electron beam,
while it passes straight through the DNA origami samples to a detector. To prepare TEM grids, 4 μl of
origami structures were deposited on a plasma cleaned grid. After four minutes, the sample was wicked
off of the grid. Finally, 10 μl and 20 μl beads of UFO and were added to the grid and it was dried. The
TEM images were obtained using an FEI Tecnai G2 Biotwin electron microscope with an electron velocity
of 80 kV.
Once well-folded structures were confirmed by gel electrophoresis and TEM, they could be used
for experiments. To avoid the reduced concentrations associated with gel purification, we used a
different purification method. For experiments folded origami structures were purified using a standard
procedure developed by Stahl et al., poly-ethylene glycol (PEG) purification [31]. PEG purification is
commonly used in other applications to purify DNA, and was applied to DNA origami fairly recently. To
PEG purify DNA origami, 15% wt/v PEG-8000 with 5 mM Tris, 1 mM ETDA, and 500 nM NaCl was mixed
with an equal volume of the folded Nanodyn. At least 200 μl of folded structure were purified. The PEG-
origami mixture was centrifuged for 25 minutes at 16,000 g and at room temperature. The supernatant
was removed from the tube using a pipette, and the resulting DNA origami pellet was resuspended in
the desired buffer. For the Nanodyn, the resuspension buffer used was typically 1x folding buffer and 10
mM MgCl2. The PEG purification procedure can be repeated an arbitrary number of times – most staples
are removed after one round, and after two rounds staples are almost nonexistent. The concentration
of the resulting PEG purified solution was measured using a nanodrop spectrophotometer [7].
Fluorescence Measurements
To quantify FRET efficiency in the Nanodyn, a HORIBA Fluoromax fluorometer was used to excite
samples with specific wavelengths of light and to measure their fluorescent output at a range of
wavelengths. The sample was excited at 510 nm and the fluorescent intensity was measured from 530 –
750 nm. This excitation wavelength will directly excite the donor, and if FRET is occurring the acceptor
will also be excited. The sample was also excited at 610 nm to directly excite the acceptor and intensity
was measured from 630 – 750 nm. The resulting spectra were processed using the ratio A method,
described elsewhere [32]. Briefly, FRET efficiency is obtained from the ratio(A) method calculating the
ratio of acceptor excitation from donor excitation to direct acceptor excitation. The method used here
also uses a blank spectra and a spectra of the bulk fluorophores to obtain a more precise measurement.
PEG purified Nanodyn samples were analyzed in a 12 μl quartz cuvette using the fluorometer.
The Nanodyn structures were present at approximately 20 nM as measured by the nanodrop. Exact
concentration measurements are not strictly necessary for fluorescence, because the ratio of emissions
is calculated. As long as the concentration is high enough to obtain clear spectra, the efficiency of
samples at differing concentrations can be compared.
The viscosity of the Nanodyn samples was controlled by varying the weight percentage of PEG-
8000 in solution. After two rounds of PEG purification, the Nanodyn was resuspended in 1x FOB at 10
mM MgCl2. Aliquots of the resulting PEG purified samples were combined in a 1:1 volumetric ratio with
solutions of PEG-8000, also at 1x FOB and 10 mM MgCl2, in order to obtain Nanodyn structures in PEG at
a known weight percent. Literature correlations for PEG viscosity were used to approximate the viscosity
of the resulting solution.
Results
Structure Folding
Following the described procedure for folding the Nanodyn, viable structures were created. The
results of gel electrophoresis comparing the scaffold with the folded structure can be seen in figure 13,
below.
Figure 13: Gel electrophoresis image showing successful folding of the Nanodyn. From left to right, the lanes are: 10 kilobase DNA ladder, 8064 scaffold, Stock Nanodyn, Newly folded Nanodyn, 10 kilobase ladder. Red box indicates similarity between new
structures and previously validated structures. Excess staples are seen near the bottom of the image.
The well-folded, compact structures travel faster than the scaffold, behavior which is consistent with
most DNA origami structures. The “stock” Nanodyn is an identical nanostructure that was previously
folded. It is used here to ensure that the newly folded structures match structures that have already
been validated in previous work. The two are not identical – there is a secondary band in the stock that
is not present in the new fold. This secondary band is probably a result or structure dimerization that
sometimes occurs over time. Given sufficient time, interactions between structures can cause them to
dimerize or aggregate. Despite the secondary band in the stock well, the results of gel electrophoresis
suggest that the newly folded Nanodyn closely resembles the previously validated structure.
To fully validate proper folding of the Nanodyn, the folded structures were PEG purified once.
TEM grids were prepared with the structures and they were imaged. A representative image of the
Nanodyn can be seen in figure 14.
Figure 14: TEM Image of several negatively stained Nanodyn structures in the open configuration.
In figure 14, both barrels of the Nanodyn can clearly be seen, with a gap of approximately 35 nm
between them in some places. This gap length is consistent with the length of the scaffold loops. The
TEM images show that there is a distribution of configurations occupied by the Nanodyn. In figure 14,
several Nanodyn are shown in a variety of open configurations.
Fluorescence
The validated structures at 20 nM were tested for bulk fluorescence across a range of PEG-8000
weight percentages. A constant salt and buffer concentration was maintained across samples to ensure
the viability of the origami. The FRET efficiency was measured as described previously. The following
image (figure 15) compares the normalized spectra of two samples, one in buffer (blue) and one in 15
wt% PEG-8000 (red). The intensities of each spectra were normalized to account for differences in
concentration between samples.
Figure 15: Bulk Fluorescence spectra for the donor and acceptor attached to the Nanodyn. The peak at 670 nm corresponds to the excitation of the donor. The red curve shows more acceptor excitation because more of the Nanodyn are closed.
The plots of direct acceptor excitation are almost identical, with a peak at 670 nm independent of PEG-
8000 concentration. When the donor is excited, there is also an identical peak at 560 nm, independent
of PEG concentration. However, the donor excitation spectra differ at 670 nm. There is a much higher
peak at 670 nm due to the addition of PEG-8000 to the solution. This peak corresponds to the acceptor,
and indicates that more FRET is occurring from donor to acceptor in the PEG solution. This most
probably indicates that more Nanodyn are closed in the more viscous solution.
Identical Nanodyn structures were diluted in a range of PEG-8000 concentrations, and the bulk
fluorescence of each was measured. The FRET efficiency of each was calculated, and the results are
shown in figure 16 and figure 17, below.
Figure 16: Nanodyn FRET Efficiency as a function of PEG-8000 weight percent.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 2 4 6 8 10 12 14 16
FRET
Eff
icie
ncy
Weight Percent PEG-8000
Nanodyn FRET Efficiency vs Weight Percent PEG-8000
Figure 17: Plot of FRET Efficiency vs Viscosity for the Nanodyn in varying PEG weight percentages. Viscosity calculated from [33], [34].
The plot (figure 17) shows a clear linear dependence of FRET efficiency on viscosity in the lower range,
before the efficiency settles to a relatively constant value around .38.
The dependence of viscosity on FRET efficiency indicates that the conformation of the Nanodyn
is sensitive to the presence of macromolecules in solution. As the space available for the Nanodyn
decreases, the entropic cost associated with the closed structure is decreased. This makes it more likely
to exist in the closed state. It is unsurprising that this dependence is essentially linear at low viscosity,
given that the Nanodyn mostly exists in an open state in buffer. However, the efficiency curve becomes
saturated, as almost all of the Nanodyn exist in the closed conformation and no more can be closed. This
corresponds with the plateau observed above 3 mPa*s. The efficiency does not reach 100% due to
several possible reasons. As previously mentioned, FRET is a strong function of distance, and there is still
some separation between fluorophores when the device is in the closed state. Further decreases in the
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 2 4 6 8 10 12 14 16
FRET
Eff
icie
ncy
Viscosity (mPa*s)
Nanodyn FRET Efficiency vs Solution Viscosity
expected efficiency could be due to the relative dipole alignment of the fluorophores or self-quenching
between the fluorophores.
Discussion
The data strongly suggest that our hypothesis is correct: The ensemble conformation of the
Nanodyn is sensitive to the presence of macromolecules in solution. However, characterizing this
sensitivity and understanding how it relates to the properties of the crowding agent is vital if the
Nanodyn is to function as a sensor. For PEG-8000, the Nanodyn has a sensitive range of approximately 1
to 3 mPa*s. At higher viscosities, the sensors are all shut and any difference in viscosity cannot be
resolved. The rheology of the cytoplasm has been studied before, and measurements are on the order
of 1 mPa*s [35], [36]. This is potentially an ideal use for the Nanodyn as described here. Collagen, a gel
and a structural component of the extracellular matrix, has a viscosity on the order of 25 mPa*s,
meaning the Nanodyn may require design alterations to enable measurements at higher viscosities [37].
Using the results obtained here, it may be possible to predict the behavior of the Nanodyn in
other solutions. If we assume that the Nanodyn and crowding agents are both homogenously
distributed in solution, then it is reasonable to suggest that the concentration where all of the Nanodyn
are closed is the same as the polymer overlap concentration. The Nanodyn changes configuration due to
excluded volume effects – if all of the Nanodyn are closed it must mean there is very little room
between crowding agents. Ziębacz et. al. report several measurements of PEG taken at a range of
molecular weights and found that the overlap concentration for PEG was related to molecular weight by
a power law relationship [38]. Interpolating from their data, the overlap concentration of PEG-8000 is
predicted to be 9.7 wt%. This value, corresponding to a viscosity of around 8 mPa*s, is approximately
double the point where all of the Nanodyn are closed. We expect that this relationship should be
maintained when other PEG molecules are used as the crowding agent, and this hypothesis will be
tested in future work.
Chapter 3: Bulk Viscoelasticity of DNA
Introduction
As a foundation for measuring the viscoelastic properties of DNA origami, we aimed to use shear
macrorheology to measure the viscoelastic behavior of dilute DNA solutions. There were several
previous publications measuring the rheology of λ-DNA (approximately 42 kilobases) at relatively high
concentrations using a rheometer, showing that it was at least plausible to apply the same method for
measuring the viscoelastic properties of staple and scaffold DNA [39], [40]. Initial tests focused on
measuring the difference in viscoelastic properties at different concentrations of λ-DNA. The goal was to
determine optimal testing conditions for smaller, lower concentration DNA samples. Therefore, the
strain (oscillation amplitude) and frequency of oscillation were varied. Although the results showed
some agreement with literature sources, the bulk rheology results demonstrated some limitations of
typical bulk rheology methods. There was no distinguishable difference in the viscoelasticity of dilute
samples at differing concentrations. The sample was also subject to evaporation, which made it difficult
to run proper experiments. Furthermore, the rheometer required relatively large sample volumes,
which would make further tests with DNA origami impractical.
Some background will be given for the use of a rheometer and the literature precedent for
measuring the rheology of DNA. The methods used in these experiments will be presented. Finally, the
results obtained will be presented and discussed.
Background:
Rheometers and Rheological Testing:
The rheometer is the go-to analytical tool for measuring viscoelastic properties in a variety of
viscoelastic fluid samples [41]. Rheometers typically measure shear properties by applying force to a
sample between two parallel plates. The rheometer has two vital components: a motor and a
transducer. The motor is required to apply precise deformation to the sample. An accurate rheometer
requires a motor that can apply very precise small and large-scale deformations, is very stiff, and has
very low run-out (eccentricity between drive shaft and plate). The motor is also coupled with an optical
encoder to measure angular displacement. As one of the plates is driven by the motor, the other is held
at zero displacement. The force required to maintain the plate at zero displacement is measured by a
transducer. State of the art transducers are non-contact and are designed to be infinitely stiff, making
them sensitive to micronewton*meter torques. Viscoelastic properties are temperature sensitive, so
rheometers also incorporate temperature controllers and sensors. A diagram of a typical rheometer is
shown in figure 18, below.
Figure 18: A representative schematic of a parallel plate rheometer. The oscillating motor typically controls the bottom plate, while the top plate senses force. The sample (green) is held between the two plates. Adapted from [42].
Several variables need to be defined to run a test on a rheometer [41]. There are two
fundamentally different modes of operation for most rheometers, which are stress controlled and strain
controlled, with the latter being more common. In stress-controlled tests, the motor is driven with a
given torque, while strain controlled tests apply a specified deformation to the sample. The two tests
should theoretically yield identical results, but apparatus design constraints makes it easier to get
accurate rheological measurements using strain control. The measurement can also be conducted using
steady shear or oscillatory shear. These two tests measure fundamentally different properties. Steady
shear only measures the amount of force required to achieve a certain shear rate, allowing the viscosity
to be calculated. For steady shear tests, either the applied torque or the shear rate is specified, while
the other quantity is measured. Oscillatory shear allows for the measurement of viscoelastic properties,
making it a much more useful test. For oscillatory shear tests, the frequency of oscillation must be
specified. Frequency and strain sweeps are common oscillatory shear tests, where frequency or strain is
varied while stress is measured.
Rheometers are usually designed to accommodate a variety of plate geometries. Parallel plates
are common, but cone-plate and couette geometries are also common (Figure 19).
Figure 19: Common rheometer geometries: parallel plates (A), cone and plate (B), couette (C). Adapted from [43].
Although the geometries are different, they all have the same operating principle: stress is calculated
from the force measured by the transducer and the contact area. Different geometries have different
areas and different sample size requirements, and apply force in different ways. Parallel plates are
simple, require relatively small sample sizes (1-2 ml), and the gap between them can be altered.
However, due to the change in velocity from the center to the edge of the plate, there is variation in the
shear rate. Cone-plate geometries provide move with a constant shear rate, but have a non-constant
gap size. Couette geometries greatly increase the contact area between the instrument and the sample,
increasing the accuracy of measurements at low viscosity. However, these geometries require large
sample volumes and have larger moments of inertia, making them incompatible with shear rate changes
or high oscillation frequency.
Viscoelasticity of DNA
There has been considerable interest in the viscoelastic properties of DNA for several years, and
various papers have been published on the topic. Mason et al. used 13 kbp calf thymus (CT) DNA over a
concentration range from 1 mg/ml to 10 mg/ml to measure the rheology of semi-dilute and entangled
DNA [44]. They first report strain sweeps at a range of concentrations from .01 radians to 10 radians at 1
rad/s and frequency sweeps from .1 rads/s to 43 rad/s at a strain of .02. They found that at low strain
conditions corresponding to linear viscoelasticity, G’ and G’’ are not functions of strain and increase with
concentration. Their results suggest that it might be possible to differentiate between different
concentrations of DNA that represent different stages in the DNA origami folding process.
Another group reported the intrinsic viscosity of small DNA duplexes (20-395 bp) using capillary
viscometry, a low-shear viscosity measurement method that measures the time it takes for a solution to
fall through a narrow tube [45]. Intrinsic viscosity is a measure of the viscosity contributions of a
molecule in solution independent of the solvent viscosity. It is calculated in the limit of zero
concentration, so it cannot be used to predict viscosity based on concentration. Based on their report,
intrinsic viscosity increases by approximately 50 times for dsDNA from 20 bp to 395 bp. They also found
that there is no non-Newtonian viscoelastic behavior in dilute double stranded DNA below
approximately 1000 base pairs.
Finally, a study published in August 2016 by Bravo-Anaya et. al. studied the viscoelastic
properties of DNA strands at a range of lengths and concentrations [46]. They found that the overlap
concentration for short DNA strands is very high, around 125 mg/ml. They also determined that short
DNA strands are typically not viscoelastic.
Methods
Rheological experiments were conducted to measure the viscoelastic properties of the DNA particularly
related to DNA origami. The scaffold is present in a typical folding reaction at 20 nM with staples at 200
nM. Given the known length of the scaffold and the approximate length and amount of staples, folding
reactions are at approximately 1 mg/ml of total DNA. Staples and scaffold are both relatively expensive
and hard to produce at volumes applicable to bulk rheology, so viscoelasticity in other types of DNA was
explored first. λ-DNA (“lambda DNA”) is a 42 kbp linear DNA duplex, which is isolated from a
bacteriophage. λ-DNA has many applications in molecular biology and can be purchased in high
concentrations relatively cheaply. CT-DNA is another common biological reagent. Large single stranded
DNA molecules are isolated and sheared to generate a homogeneous but polydisperse solution DNA
with an average length of approximately 2 kbp. The rheology of both λ-DNA and CT-DNA has been
studied extensively, and both are much cheaper than scaffold or staples molecules, so initial rheological
tests were performed on these solutions.
Rheological Measurements
Solutions of λ-DNA and CT-DNA were diluted in their respective storage buffers to the desired
concentration. λ-DNA was suspended in 1X TE buffer (10 mM tris-HCl, 1 mM EDTA) while CT-DNA was
suspended in ddH2O. An ARES G2 rheometer in Dr. Kurt Koelling’s lab was used to conduct bulk
rheological measurements. Parallel plates (Diameter = 25 mm) were used for all tests. Initially, the
experimental goal was to determine the ideal testing conditions for dilute DNA, so frequency and strain
sweeps were conducted. For frequency sweeps, the strain was held constant at 1, 10, or 100 radians
while strain rate was varied from 0.1 to 100 rad/s. For strain sweeps, the frequency was held constant at
1, 10, or 100 rad/s while the strain was varied from .1 to 500 radians. The upper limit on strain was
governed by the ability of the rheometer to accurately rotate the plate.
To actually perform measurements, a sample was transferred from an epi tube to the plate
using a pipette. The sample was pipetted up and down several times to mix it before transfer.
Approximately 1 ml of sample was added to the plate, although the volume was not precisely controlled.
The constraint on volume was related to the size of the plate – ideally, the gap between plates was
between 1 and 2 mm, corresponding to a volume between 0.5 and 1 ml. After loading the sample, the
top plate was lowered towards the bottom until the top plate touched the sample. The top plate was
then very slowly lowered until the sample formed a uniform column. A test was then conducted over a
time span of 1 to 5 minutes. The total time was a function of the frequencies and strains involved in the
test. After a test was conducted, the gap was narrowed slightly to account for evaporation before
another test was conducted. After all tests had been run on a given sample, the remaining sample was
collected using a pipette and used in later experiments.
Results The results of identical strain sweeps at several λ-DNA concentrations are shown in figure 20,
below. The strain sweeps were conducted from .05 radians to 500 radians at a frequency of 1 rad/s.
Figure 20: The results of changing DNA concentration on the stress-strain relationship of the solution. Newtonian fluids have a constant linear stress-strain relationship. A decrease in slope is indicative of shear thinning. Error bars represent one standard
deviation based on three replicates.
There are several obvious observations from figure 20. First, higher DNA concentrations require more
force to deform for a given strain and therefore are more viscous. This is both intuitively and
theoretically expected. The figure also shows deviations from Newtonian behavior at the highest
concentration. The correlation between stress and strain in Newtonian fluids should be linear and
constant. At 0.5 mg/ml concentration, the slope decreases at higher strain. This non-Newtonian
behavior is known as shear thinning and is characteristic of linear polymers. As the polymer is deformed,
they stretch to a more linear conformation and require less force to deform further, leading to the
observed decrease in viscosity. This is also dependent on the shear rate.
0.001
0.01
0.1
1
1 10 100
Stre
ss (
Pa)
Strain (radians)
Variation in Newtonian Behavior at Varying λ-DNA Concentrations for Strain Sweeps at 1 rad/sec
0.5 mg/ml 0.2 mg/ml 0.04 mg/ml 0.004 mg/ml Buffer
Figure 20 also gives some insight to the resolution of the rheometer. The required stress and
corresponding viscosity decrease with concentration, but the ability to distinguish between
concentrations based on the rheological measurements shown here is tenuous at best below 0.2 mg/ml.
DNA origami folding reactions contain 0.05 mg/ml large scaffold and 0.45 mg/ml short staples, for about
0.5 mg/ml total DNA. However, the staples are in 10x excess and only 10% of them will bind with the
scaffold under ideal conditions. Therefore, the rheometer ideally needs to detect viscoelastic differences
between solutions in the µg/ml range.
There was also evidence of viscoelasticity in λ-DNA, as is shown by the changing elastic and
viscous moduli shown in strain sweeps. The following figure, from reference 44, shows how
viscoelasticity is effected by strain in long (13 kbp) DNA strands. The DNA studied in figure 21 has an
overlap concentration of approximately 0.7 mg/ml, so the range of values tested are all above the
entanglement concentration of the DNA.
Figure 21: Plot of G' and G'' of 13 kbp DNA strands measured in an oscillatory strain sweep on a shear rheometer. Solid symbols are for G’, while open symbols are G’’. The oscillatory frequency was fixed at 1 rad/s. 1 dyne/cm2 is equivalent to 0.1 Pa*s.
Modified from [44].
Figure 21 serves as a reference for the strain sweep tests conducted here on λ-DNA. The concentration
of λ-DNA used varied from 0.004 mg/ml to 0.5 mg/ml. Calculations indicate that the overlap
concentration of λ-DNA should be approximately 0.25 mg/ml, so viscoelastic behavior should be
prominent above this concentration in the samples studied here. A plot of the viscous and elastic moduli
(Figure 22) show this to be the case.
Figure 22: Viscoelastic Moduli from strain sweep of λ-DNA at varying concentration. The data show a decrease in the storage and loss moduli as concentration is decreased. Noise in the measurement prevented data from lower concentrations being
added. Error bars represent 1 standard deviation based on 3 replicates.
Figure 22 shows how the storage and loss moduli changed with increasing strain at different
concentrations. The measurements were noisy, especially at low concentrations and strains, to the point
that the data was omitted from the plot. However, the data shown agrees qualitatively with the data
0.001
0.01
0.1
1
10 100 1000
G',
G''
(Pa)
Strain (radians)
Viscoelasticity in λ-DNA at Varying Concentrations - Strain Sweep
G' - 0.5 mg/ml G' - 0.2 mg/ml
G'' - 0.5 mg/ml G'' - 0.2 mg/ml G'' - .04 mg/ml
shown in figure 21. At the highest concentration, a plateau in G’ and G’’ is observed at low strain around
.1 Pa, with G’ dominating. The plateau drops off around 100 radians, with G’’ starting to dominate at the
crossover strain of 250 radians. Although the plateau moduli are not observed in the 0.2 mg/ml sample,
there appears to be a crossover strain between 80 and 125 radians, less than the value for the higher
concentration. Finally, the magnitude of both moduli dropped with concentration. All of these results
agree with theory and with other studies, and confirm that solutions of large DNA strands are
viscoelastic. However, the applicability of the λ-DNA tests is questionable because λ-DNA is much longer
than either the scaffold or the staple molecules currently used in DNA origami, and viscoelastic
properties are strong functions of polymer length.
CT-DNA solutions were also studied using bulk rheometry. Higher concentrations were able to
be studied due to the stock concentration of CT-DNA. However, the data in general was noisier for CT-
DNA due to the much shorter chains. For instance, the results of stress-strain relationship of three
separate strain sweeps, each replicated three times total, can be seen in the following figure.
Figure 23: Average stress vs strain for triplicate strain sweeps of 3 mg/ml CT-DNA at 3 frequencies. Both 1 rad/sec and 10 rad/sec were very noisy, and no signal was detected at 100 rad/sec at low strain.
The data show that it is impossible to measure stress at low frequencies, even for relatively highly
concentrated DNA. However, it also shows that there is no distinguishable shear-thinning in the short
DNA strands studied here. There are two interpretations for this behavior. The shorter DNA strands
could be so small that they are essentially rigid on the scale of shear forces relevant to this work and do
not change orientation appreciably when shear is applied. Alternatively, they could be capable of the
same non-Newtonian behavior that was observed in longer DNA. However, given that the individual
molecules are shorter, unaligned particles experience less drag and therefore take longer to align. This
second possibility is in agreement with literature.
0.01
0.1
1
10
0.01 0.1 1 10 100 1000
Stre
ss (
Pa)
Strain (radians)
Stress vs. Strain in Strain Sweeps at 3 Frequencies - 3 mg/ml CT-DNA
1 rad/sec
10 rad/sec
100 rad/sec
The elastic and viscous moduli of CT-DNA support the previous observation that measuring the
viscoelasticity of short DNA strands using a bulk rheometer may be difficult (Figure 24). There was no
discernible pattern in either G’ or G’’ as a function of CT-DNA concentration.
Figure 24: Comparison of viscoelastic moduli in CT-DNA at varying concentrations. The data is very noisy, and it appears as though the elastic and viscous moduli are constant over the range of strains studied here.
Figure 24 shows that the elastic and viscous moduli depend very little on strain, indicating that the
material is linearly viscoelastic in this range of strains.
Discussion
These tests show that DNA can be studied as a polymer. It has polymeric viscoelasticity and
undergoes shear thinning. These factors are crucial for understanding fundamental biophysical
0.1
1
10
10 100 1000
G',
G''
(Pa)
Strain (radians)
Viscoelasticity in CT DNA at Varying Concentrations - G' and G'' vs Strain at 100 rad/sec
3 mg/ml - G' 1 mg/ml - G' .1 mg/ml - G'
3 mg/ml - G'' 1 mg/ml - G'' .1 mg/ml - G''
questions. For instance, DNA organization in the nucleus is fundamentally related to the stiffness of the
DNA helix and other rheological factors. The structure of polymers is also fundamentally related to
transport properties in polymer solutions, meaning that an improved understanding of DNA polymer
dynamics could improve our understanding of the influence of regulatory molecules which work in the
nucleus.
The results here do not support the hypothesis that DNA origami folding can be studied using
bulk rheology. Based on the data gathered from these experiments, there are two independent
conclusions which can be drawn. First, the origami staples, which make up 90% of the DNA in solution,
are not appreciably viscoelastic. Second, it is unlikely that the rheometer used here will be able to detect
the extremely subtle changes in material properties that should accompany DNA origami folding. One
possibility would be to improve some of the control or measurement elements on the rheometer, but
the noise associated with the samples that were tested in these experiments was substantial and
probably will not be remedied by incrementally improved transducers or motors.
There are also several problems inherent to the method that suggest it is not applicable for DNA
origami. Firstly, there is the problem of evaporation. As the sample sits between the rheometer plates, it
is constantly evaporating. Slight evaporation can be accounted for by changing the plate gap. It can also
be mitigated by isolating the rheometer plates and adding a solvent trap to the chamber. The solvent
trap controls the humidity in the chamber and slows the rate of evaporation, but it remains a nuisance
variable. More importantly, the sample size requirements for bulk rheology are almost certainly
prohibitive. Neither scaffold nor staples are cheap, and the sample size and concentration requirements
for a rheological measurement are both much larger than is typical for DNA origami folding.
Chapter 4: Microrheology of DNA
Viscoelasticity is generally a property of the molecular scale structure and interactions in a
material. Rheometers probe this structure by measuring the bulk material response to imposed force,
but they are not the only measurement method. Microrheology in general refers to the variety of
methods that measure the rheology of a substance by studying the behavior of microscopic particles
suspended in that substance. Microrheological experiments have many benefits compared to
experiments conducted on a rheometer. For one, they require very small samples – on the order of 10
μl. They also allow for the characterization of materials at different length scales, something that bulk
rheology cannot do.
Background
Microrheology relies on the connection between two derivations for the diffusivity of a particle
in a viscous solution. Here we present the mathematical background of microrheology. It also involves
the use of particle tracking hardware and software. Video microscopy will be introduced, along with the
workflow for extracting rheological measurements from videos.
The Mathematics Behind Particle Diffusion
Particle tracking microrheology relies on two separate equations that predict the behavior of
molecules or particles experiencing Brownian motion. One of these, the Stokes-Einstein relationship, is
derived from first principles based on the collisions experienced by the bead. The other expression is
derived from Fick’s law and the assumption that the bead diffuses randomly through a material.
In 1905, Einstein published his dissertation on the motion of particles [47]. He showed that the
diffusion of a bead in solution was a function of only temperature and the shape of the bead. He derived
an expression for the diffusivity of a bead that was a function of bead shape and temperature:
𝐷 =
𝑘𝐵𝑇
𝜉
(12)
Where D is particle diffusivity, also referred as the diffusion constant, and ξ is a friction factor for the
particle representing the ratio of particle velocity to drag force in solution. The friction factor for a
spherical bead is given by Stokes law [48]:
𝜉 = 6𝜋𝜂𝑟 (13)
where η is the solution viscosity and r is the particle radius. Stokes law is valid for small particles at low
Reynolds numbers. The Stokes-Einstein equation for bead diffusivity is therefore:
𝐷 =
𝑘𝐵𝑇
6𝜋𝜂𝑟
(14)
The diffusion of a particle can also be derived independently from continuum mass transport
using Fick’s law and conservation of mass [49]. 1-dimensional diffusion can be used as a representative
derivation. Diffusion in 1-D is governed by the following equation:
𝜕𝑐
𝜕𝑡= 𝐷
𝜕2𝑐
𝜕𝑥2
(15)
For a concentration of c0 at a position of x=0 at time t = 0, the concentration profile at a future time t is
given by:
𝑐(𝑥, 𝑡) =
𝑁
√4𝜋𝐷𝑡∗ exp(−
𝑥2
4𝐷𝑡)
(16)
𝑁 =
𝑐0(𝑥)
𝛿(𝑥)𝑎𝑡𝑡 = 0
(17)
N is the total number of particles in the sample, which are assumed to be placed at x=0 at the initial
time.
Equation 16 describes how the distribution of particles will spread out over time, but it can also
be thought of as a probability distribution for finding an individual particle at location x and time t.
Specifically the probability of finding a particle in an infinitesimally small slice of the x-axis is based on
the total amount of particles and their initial concentration:
𝑃(𝑥)𝑑𝑥 =
𝑐(𝑥)
𝑁𝑑𝑥
(17)
The expectation value for the position of a particle in 1-D diffusion is given by:
⟨𝑥2⟩ = ∫ 𝑥2 ∗ 𝑃(𝑥)𝑑𝑥
∞
−∞
(18)
⟨𝑥2⟩ = ∫
𝑥2
√4𝜋𝐷𝑡exp(−
𝑥2
4𝐷𝑡)𝑑𝑡
∞
−∞
(19)
⟨𝑥2⟩ = 2𝐷𝑡 (20)
The expected value of a particle in 1-D diffusion is a function of time and the diffusivity of the particle.
The equipartition theorem shows that the constant multiple is a function of the dimension; it is four for
2-D diffusion and six for 3-D diffusion. The root-mean-square displacement of a particle in 2-D diffusion
is then:
𝑥𝑅𝑀𝑆𝐷 = √4𝐷𝑡 (21)
Two equations have been derived which relate to the diffusivity of a particle in viscous media at
low Reynolds numbers. The goal is still to measure viscoelastic properties of solutions, so combining
those expressions (equations 21 and 14) and solving for viscosity yields:
𝜂 =
𝑘𝐵𝑇
6𝜋𝑟∗
4𝑡
⟨𝑥𝑅𝑀𝑆𝐷⟩2
(22)
Using that equation, the viscosity of a solution can be calculated if several variables are known.
Temperature can be measured easily. Microscale beads can be purchased which will satisfy all of the
conditions for Stokes drag, and the radius of these beads should be known. If the Root mean squared
displacement of the bead can be measured over time, the solution viscosity can be calculated. The
method described here can be used for calculating pure viscosity, but it can be extended to measure
viscoelastic properties by calculating the frequency dependence of bead displacements [50].
Particle Tracking
In order to calculate the bead RMSD, video microscopy and particle tracking algorithms are
used. Video microscopy is essentially the capture of microscopic images with a high framerate, but the
details of implementation may vary. For microrheology, the video microscopy system needs to be able
to capture images with high enough resolution to differentiate between beads as small as 100 nm in
diameter. Depending on the application, using fluorescence to excite fluorophores on the surface of a
bead may improve image quality. For instance, a thick polymer network might interfere with following
the trajectory of a bead using bright-field microscopy, but fluorescence may allow the particle to be
tracked.
After bead motion has been captured on video, frame by frame image processing can extract
the trajectory. There are several general steps a particle tracking algorithm must follow. The video
frames the tracking algorithm takes in are given thresholds, meaning that any pixel above a certain value
is set to black and any pixel below a certain value is set to white. A bandpass filter is used to remove
high-frequency noise from the image. The particles can then be identified in the processed image.
Some particle tracking algorithms have automatic particle identification, but the method used
here relied on human input of a particle location in the first video frame. After manual location selection
the next frame in the video was processed identically. Based on the location of the particle in the
previous frame, the location of the maxima nearby that location in the current frame, and the
distribution of intensities around the maxima, the particle position is determined in this frame. The
algorithm is repeated for each frame in the video until the end is reached. In this way, particle position
can be tracked over time. The resulting trajectory can be analyzed to extract the root mean square of
position.
Methods
To prepare a microrheological experiment, a sample had to be prepared. The sample then had
to be imaged, and the resulting images had to be processed and analyzed to extract particle trajectories.
Sample Preparation
To prepare a sample, 5 μl of fluorescent bead suspension was vortexed and combined with the
desired sample at 2X concentration in a 1:1 ratio. The fluorescent beads had a nominal radius of 0.5 µm
and fluoresced under 561 nm light. The fluorescent bead stock was mixed at a volume fraction of 10-4
beads. After the beads were added to the sample, 5 μl of the sample was added to a slide and a 22mm x
22mm glass coverslip was applied to the solution. Compressed air was used to remove dust from both
the slide and the coverslip. After the sample had spread under the coverslip, the coverslip was moved to
ensure that no air bubbles were present in the sample and that the sample was evenly distributed. Nail
polish was applied at the edge of the slide and allowed to dry in order to seal it.
Microscopy and Image Processing
A Nikon eclipse Ti-E total internal fluorescence microscope (TIRF) system was used to image the
fluorescent beads in TIRF mode. The beads were excited using a 561 nm laser. AVI video was acquired at
multiple locations on the slide. Videos were typically taken over ten seconds at 30 frames per second
and a magnification of 100x. Locations were ideally selected that had several beads in frame to minimize
image processing.
After video was recorded it was processed using a MATLAB script. After images had been
processed with MATLAB, the trajectories were examined and compared with the video footage.
Occasionally, particles would leave the focal plane of the microscope during the video, leading to
aberrant trajectories. These trajectories were discarded and the mean square displacement of each
particle was calculated from the remaining trajectories. The average particle displacement was the
calculated and the particle diffusivity was fit using equation 22.
Results
The initial goal of microrheological tests was to validate the method. Therefore, the viscosity of
water was measured first. By using the TIRF microscope, video footage was taken of bead diffusion
which was able to be processed by the MATLAB particle tracking algorithm described previously. A
sample frame from a video is shown in figure 25.
Figure 25: Left: Representative frame of a microscopy video used for particle tracking. Right: Trajectories aquired from MATLAB particle tracking script.
After capturing several videos, the trajectories of particles were analyzed in MATLAB. The resulting
trajectories and RMSD can be seen in the following figure (figure 26).
Figure 26: The trajectory of ten tracked beads is shown. In the picture above, the particle was tracked over 50 seconds. The displacement shown corresponds to a diffusivity of 2.28 µm2/sec.
Initial tests using particle tracking microrheology show that the viscosity of water and glycerol
can be calculated. The results are shown in figure 27.
Figure 27: The difference between accepted literature values and measured values for the viscosity of water and 10% glycerol.
Clearly, the microrheological tests need to be improved significantly before they will be a feasible
replacement for bulk rheology. However, there are several potential causes for the deviation in
measured viscosity. Firstly, the particles could be close to the surface of the slide, meaning their motion
is not totally Brownian. This would slow the particles, leading to a decrease in measured diffusivity and a
resulting increase in viscosity. Modifications to slide prep, such as sandwiching the sample between
pieces of double sided tape to make a wider channel, could be effective.
Discussion
Quantitatively, the data gathered here leaves a lot to be desired. However, several examples
from literature suggest that this method is worth pursuing. This preliminary work did show that
diffusivity can be measured and validated the general workflow. With further optimization and
literature review, the method should provide much more accurate measurements of viscosity.
There are several reasons to think that the method is both applicable to DNA origami and worth
pursuing over macrorheology. The small sample size required is very attractive. Similar particle tracking
methods can allow for the measurement of viscoelastic properties beyond simple viscosity. Taking the
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Water 10% Glycerol
Vis
cosi
ty (
mP
a*s)
Comparison Between Microrheology and Accepted Values
Accepted Measured
Fourier transform of the RMSD trajectory yields a power spectrum, which allows for the calculation of G’
and G’’. This mathematical technique is commonly combined with optical trapping microrheology, which
measures the position deviations for a bead held in place by an optical trap. Optical trapping requires
more equipment than basic particle tracking microrheology, but it is a well-established technique.
The method can also yield measurements that are fundamentally unobtainable using
macrorheology. Bulk macrorheology measures how the sample as a whole dissipates and stores force.
On the other hand, microrheology is sensitive to length scales within the sample, and different
viscoelastic characteristics can be measured by probing the system in different ways. Liu et. al. use
microrheology to measure viscoelasticity in actin networks of varying average filament lengths [51].
They found that studying the correlation of diffusion for two distant particles gave measurements that
were in agreement with bulk rheology and constant with varying filament length. They also measured
the diffusivity of single particles, and found that single particle diffusivity was correlated with actin
length. The correlation of two particles is a result of longer timescale interactions in the actin network,
which single particle microrheology is not sensitive to. Differentiating between the material behavior at
these length scales may be useful for the study of DNA origami. Given that the individual DNA molecules
are packed relatively tightly upon folding, there would be very little long distance correlation between
the diffusion of particles after folding.
Conclusions and Future Work
The overall objective of this thesis was to explore the connection between microscale structural
characteristics of materials and their macroscale behavior in the context of DNA origami. Chapter one
presented preliminary results that demonstrate the use of DNA origami for measuring rheological
behavior. If the Nanodyn can be fully characterized, it should be able to provide valuable biophysical
information.
Future work will focus on three primary aspects of the Nanodyn. Firstly, the response of the
Nanodyn will be measured using a variety of crowding agents. We hypothesize that the structure of the
crowding agent should determine how it affects the Nanodyn. Further, because DNA is charged the
charge, polarity, and other chemical properties of the crowding agent will mediate the Nanodyn
response. In order to take quantitative measurements using the Nanodyn, all of these effects must first
be quantified. Along with variations in crowding agent, variations in the Nanodyn will also be explored.
As shown in figure 11, each linker can be constrained individually. The energetic interactions of the
fluctuating linker can also be modified by changing the staple length. If these factors are quantified, the
useful range of the Nanodyn may be increased. Finally, the design of the Nanodyn may be modified.
Changing the size of the barrel or the gap between barrels should change the sensitivity of the device.
The rheology of DNA also warrants further study. Although measuring viscoelastic changes as
folding progresses may not be realistic, there are several interesting questions that rheology could help
answer. For instance, we have found that molecular crowding can inhibit DNA origami folding. An
experiment was performed The experiment showed that structure folding completely stopped above a
certain concentration – possibly because solution viscosity inhibited staple diffusion.
To answer questions relating to viscoelasticity and DNA origami, work should focus on the
development and improvement of microrheology. A full factorial experiment for particle size and
surface chemistry could be performed to ensure that particles are compatible with DNA. The results of
the experiment should be confirmed using bulk rheology. Potentially the optical trap we have could be
calibrated, allowing viscoelastic measurements of DNA to be conducted. Ideally, an experimental
procedure and setup allowing for the determination of DNA viscoelasticity will be produced.
Bibliography [1] L. Pray, “Discovery of DNA Structure and Function: Watson and Crick,” Nat. Educ., vol. 1, no. 100,
2008. [2] J. D. Watson and F. H. Crick, “Molecular structure of nucleic acids; a structure for deoxyribose
nucleic acid,” Nature, vol. 171, no. 4356, pp. 737–738, Apr. 1953. [3] P. Yakovchuk, “Base-stacking and base-pairing contributions into thermal stability of the DNA
double helix,” Nucleic Acids Res., vol. 34, no. 2, pp. 564–574, Jan. 2006. [4] N. C. Seeman, “Nucleic acid junctions and lattices,” J. Theor. Biol., vol. 99, no. 2, pp. 237–247, Nov.
1982. [5] P. W. K. Rothemund, “Folding DNA to create nanoscale shapes and patterns,” Nature, vol. 440, no.
7082, pp. 297–302, Mar. 2006. [6] S. M. Douglas, H. Dietz, T. Liedl, B. Högberg, F. Graf, and W. M. Shih, “Self-assembly of DNA into
nanoscale three-dimensional shapes,” Nature, vol. 459, no. 7245, pp. 414–418, May 2009. [7] C. E. Castro et al., “A primer to scaffolded DNA origami,” Nat. Methods, vol. 8, no. 3, pp. 221–229,
Mar. 2011. [8] X. Wei, J. Nangreave, and Y. Liu, “Uncovering the Self-Assembly of DNA Nanostructures by
Thermodynamics and Kinetics,” Acc. Chem. Res., vol. 47, no. 6, pp. 1861–1870, Jun. 2014. [9] H. Li, T. H. LaBean, and K. W. Leong, “Nucleic acid-based nanoengineering: novel structures for
biomedical applications,” Interface Focus, vol. 1, no. 5, pp. 702–724, Oct. 2011. [10] J. Bath, S. J. Green, K. E. Allen, and A. J. Turberfield, “Mechanism for a Directional, Processive, and
Reversible DNA Motor,” Small, vol. 5, no. 13, pp. 1513–1516, Jul. 2009. [11] S. M. Douglas, I. Bachelet, and G. M. Church, “A logic-gated nanorobot for targeted transport of
molecular payloads,” Science, vol. 335, no. 6070, pp. 831–834, Feb. 2012. [12] A. Kuzuya, R. Watanabe, Y. Yamanaka, T. Tamaki, M. Kaino, and Y. Ohya, “Nanomechanical DNA
Origami pH Sensors,” Sensors, vol. 14, no. 10, pp. 19329–19335, Oct. 2014. [13] P. D. Halley et al., “DNA Origami: Daunorubicin-Loaded DNA Origami Nanostructures Circumvent
Drug-Resistance Mechanisms in a Leukemia Model (Small 3/2016),” Small, vol. 12, no. 3, pp. 307–307, Jan. 2016.
[14] Q. Zhang et al., “DNA Origami as an In Vivo Drug Delivery Vehicle for Cancer Therapy,” ACS Nano, vol. 8, no. 7, pp. 6633–6643, Jul. 2014.
[15] J. Song et al., “Isothermal Hybridization Kinetics of DNA Assembly of Two-Dimensional DNA Origami,” Small, vol. 9, no. 17, pp. 2954–2959, Sep. 2013.
[16] A. E. Marras, L. Zhou, V. Kolliopoulos, H.-J. Su, and C. E. Castro, “Directing folding pathways for multi-component DNA origami nanostructures with complex topology,” New J. Phys., vol. 18, no. 5, p. 55005, May 2016.
[17] C. Bouchiat, M. D. Wang, J.-F. Allemand, T. Strick, S. M. Block, and V. Croquette, “Estimating the Persistence Length of a Worm-Like Chain Molecule from Force-Extension Measurements,” Biophys. J., vol. 76, no. 1, pp. 409–413, Jan. 1999.
[18] L. Zhou, A. E. Marras, C. E. Castro, and H.-J. Su, “Pseudorigid-Body Models of Compliant DNA Origami Mechanisms,” J. Mech. Robot., vol. 8, no. 5, p. 51013, May 2016.
[19] P. E. Rouse, “A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers,” J. Chem. Phys., vol. 21, no. 7, p. 1272, 1953.
[20] M. O. Steinhauser and S. Hiermaier, “A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics,” Int. J. Mol. Sci., vol. 10, no. 12, pp. 5135–5216, Dec. 2009.
[21] Q. Ying and B. Chu, “Overlap concentration of macromolecules in solution,” Macromolecules, vol. 20, no. 2, pp. 362–366, Mar. 1987.
[22] D. Marenduzzo, K. Finan, and P. R. Cook, “The depletion attraction: an underappreciated force driving cellular organization,” J. Cell Biol., vol. 175, no. 5, pp. 681–686, Dec. 2006.
[23] D. Miyoshi and N. Sugimoto, “Molecular crowding effects on structure and stability of DNA,” Biochimie, vol. 90, no. 7, pp. 1040–1051, Jul. 2008.
[24] Q. Mei et al., “Stability of DNA Origami Nanoarrays in Cell Lysate,” Nano Lett., vol. 11, no. 4, pp. 1477–1482, Apr. 2011.
[25] M. Hudoba, “Force Sensing Applications of DNA Origami Nanodevices,” Ph.D Dissertation, The Ohio State University, Columbus, Ohio, 2016.
[26] K. R. Levental et al., “Matrix Crosslinking Forces Tumor Progression by Enhancing Integrin Signaling,” Cell, vol. 139, no. 5, pp. 891–906, Nov. 2009.
[27] A. E. Marras, L. Zhou, H.-J. Su, and C. E. Castro, “Programmable motion of DNA origami mechanisms,” Proc. Natl. Acad. Sci., vol. 112, no. 3, pp. 713–718, Jan. 2015.
[28] T. Förster, “Energy migration and fluorescence,” J. Biomed. Opt., vol. 17, no. 1, p. 11002, 2012. [29] R. Roy, S. Hohng, and T. Ha, “A practical guide to single-molecule FRET,” Nat. Methods, vol. 5, no. 6,
pp. 507–516, Jun. 2008. [30] P. Held, “An Introduction to Fluorescence Resonance Energy Transfer (FRET) Technology and its
Application in Bioscience,” 2012. [31] E. Stahl, T. G. Martin, F. Praetorius, and H. Dietz, “Facile and Scalable Preparation of Pure and Dense
DNA Origami Solutions,” Angew. Chem., vol. 126, no. 47, pp. 12949–12954, Nov. 2014. [32] R. M. Clegg, “Fluorescence resonance energy transfer and nucleic acids,” Methods Enzymol., vol.
211, pp. 353–388, 1992. [33] P. Gonzalez-Tello, F. Camacho, and G. Blazquez, “Density and Viscosity of Concentrated Aqueous
Solutions of Polyethylene Glycol,” J. Chem. Eng. Data, vol. 39, no. 3, pp. 611–614, Jul. 1994. [34] F. Han, J. Zhang, G. Chen, and X. Wei, “Density, Viscosity, and Excess Properties for Aqueous
Poly(ethylene glycol) Solutions from (298.15 to 323.15) K,” J. Chem. Eng. Data, vol. 53, no. 11, pp. 2598–2601, Nov. 2008.
[35] S. Bicknese, N. Periasamy, S. B. Shohet, and A. S. Verkman, “Cytoplasmic viscosity near the cell plasma membrane: measurement by evanescent field frequency-domain microfluorimetry,” Biophys. J., vol. 65, no. 3, pp. 1272–1282, Sep. 1993.
[36] A. M. Mastro, M. A. Babich, W. D. Taylor, and A. D. Keith, “Diffusion of a small molecule in the cytoplasm of mammalian cells,” Proc. Natl. Acad. Sci. U. S. A., vol. 81, no. 11, pp. 3414–3418, Jun. 1984.
[37] Y. Li, C. Qiao, L. Shi, Q. Jiang, and T. Li, “Viscosity of Collagen Solutions: Influence of Concentration, Temperature, Adsorption, and Role of Intermolecular Interactions,” J. Macromol. Sci. Part B, vol. 53, no. 5, pp. 893–901, May 2014.
[38] N. Ziębacz, S. A. Wieczorek, T. Kalwarczyk, M. Fiałkowski, and R. Hołyst, “Crossover regime for the diffusion of nanoparticles in polyethylene glycol solutions: influence of the depletion layer,” Soft Matter, vol. 7, no. 16, p. 7181, 2011.
[39] C. M. Schroeder, E. S. G. Shaqfeh, and S. Chu, “Effect of Hydrodynamic Interactions on DNA Dynamics in Extensional Flow: Simulation and Single Molecule Experiment,” Macromolecules, vol. 37, no. 24, pp. 9242–9256, Nov. 2004.
[40] J. S. Hur, E. S. G. Shaqfeh, H. P. Babcock, D. E. Smith, and S. Chu, “Dynamics of dilute and semidilute DNA solutions in the start-up of shear flow,” J. Rheol., vol. 45, no. 2, p. 421, 2001.
[41] J. M. Dealy and K. F. Wissbrun, Melt rheology and its role in plastics processing: theory and applications. Boston, Mass.: Kluwer Academic, 1999.
[42] L. Sherman, “Novel Rheometer Tells More About Thermoplastic Processing Behavior,” Plastics Technology, Sep-2005.
[43] S. Kohl, “Using Rheology to Improve Manufacturing,” Ceramic Industry, vol. 152, no. 3, p. 19, Mar-2002.
[44] T. G. Mason, A. Dhople, and D. Wirtz, “Linear Viscoelastic Moduli of Concentrated DNA Solutions,” Macromolecules, vol. 31, no. 11, pp. 3600–3603, Jun. 1998.
[45] A. Tsortos, G. Papadakis, and E. Gizeli, “The intrinsic viscosity of linear DNA,” Biopolymers, vol. 95, no. 12, pp. 824–832, Dec. 2011.
[46] L. Bravo-Anaya, F. Pignon, F. Martínez, and M. Rinaudo, “Rheological Properties of DNA Molecules in Solution: Molecular Weight and Entanglement Influences,” Polymers, vol. 8, no. 8, p. 279, Aug. 2016.
[47] A. Einstein, “<<Eine>> neue Bestimmung der Moleküldimensionen,” 1905. [48] G. K. Batchelor, An introduction to fluid dynamics, 1. Cambridge mathematical ed., 14. print.
Cambridge: Cambridge Univ. Press, 2010. [49] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport phenomena, Rev. 2. ed. New York: Wiley,
2007. [50] T. G. Mason, K. Ganesan, J. H. van Zanten, D. Wirtz, and S. C. Kuo, “Particle Tracking Microrheology
of Complex Fluids,” Phys. Rev. Lett., vol. 79, no. 17, pp. 3282–3285, Oct. 1997. [51] J. Liu et al., “Microrheology Probes Length Scale Dependent Rheology,” Phys. Rev. Lett., vol. 96, no.
11, Mar. 2006.